How to install Windows on new HD without CD player?

I've got a touch screen all-in-one computer that I use at work as our employee time clock. The hard drive crashed on it recently. I've purchased and installed the new hard drive, but the computer does not have a CD or floppy drive.

How can I install Windows in a bass ackward way?

I have a Maxtor One Touch external hard drive, if I put the Windows install file on that, would it be possible to boot the computer from that and transfer the information?

Yes, that will work.
Connect the external drive to a different computer and use SYS x: to put a bootable DOS on it (from XP or NT you can't do this; you may have to boot DOS).
Xcopy the entire i386 directory from the CD to the drive.
Then connect the drive to the machine, you should be able to boot from it.

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